 Now here is experiment number three. In experiment number three, you have a loop with a galvanometer like this. The magnetic field is like this, B. Okay? Somehow you are creating the magnetic field. Now what you are doing is, you are changing magnetic field with time. B changes with time. B started to change. Fine? Or you can say that whatever was the B earlier, you switch it off and it becomes zero. B was a magnetic field, it became zero the next moment. Fine? But the galvanometer showed the deception. What does it mean? Is magnetic field changing in 1 and 2? Yes or no? Magnetic field through the coil should change. So the conclusion three is magnetic field through coil should change for current to be generated. Can you tell till now? Now let's talk about the final experiment. Experiment number four. Magnetic field is coming out like that. Okay? B is constant. Magnetic field is constant now. What you are doing is, you are making it shrink. As in next moment it is like this. The coil, you are compressing it. Fine? Magnetic field B is constant throughout the surface. You compressed it and galvanometer showed the deflection. Now what should be the conclusion? Think over it and then speak. The final conclusion. Sir, is it a regular flux? Is flux changing here? Reading it. So basically it is not about magnetic field. It is about? Magnetic flux. Not even that. Change in flux. The change is important. If you keep magnetic field constant, very high magnetic field, current will not get generated. Fine? The flux should change. So the final conclusion is change in magnetic flux. Fine? This is our final conclusion and from there on the chapter starts. How we calculated electric flux, you remember? Electric flux, how we calculated? Phi E. That is equal to q by epsilon naught. But what it is? Integral of E dot dA. Fine? This was a flux and this was a flux through encloses or enclosure. Fine? Can you tell me how much is the flux this is equal to? It is given by Gauss law. This is q enclosed by epsilon naught. Can you tell me how much is the magnetic flux in an enclosure? This is for electric flux. How much should be the b dot dA integral? That should be equal to what? d dot dA through a closed surface. So net flux through the closed surface due to magnetic field is what? It is 0 because there is no monopole exist. Counter part of charge is not there. Every time you enclose a magnet, north and south pole both get enclosed. It is like enclosing dipole, electric dipole in the enclosure. Total charge enclosed will be 0. So if you integrate this magnetic flux through the 3D enclosure, it will always be equal to 0. Fine? But when we have taken the examples, was that an enclosure? The flux, it was not an enclosure. It was a loop. It was a loop. What is the difference between loop and then 3D enclosure? Because what is the difference? Loop is 2D? 2D. Just because I told you 3D enclosure is a little bit too big. If I take a loop and put half of it here and half of it here, does it become 3D? Yes or no? Yes. It becomes 3D? Yes, 3D, but what is the difference between loop? It does not have a surface. It does not have a surface. It has just a line which enclosed it, but it need not be 2D. So it is not closed from 3 dimensionally. It does not have a surface to enclose. To enclose, you need a surface. So when I talk about magnetic flux, what I do? I calculate through the loop. I do not calculate through the 3D enclosure. Basically magnetic flux is calculated in loop, not for 3D enclosure like we have done in the case of Gauss law. But then magnetic flux has also area vector. It is like d dot dA. So what is this area? If there is no surface area, what is this? Area enclosed by the loop. And if the entire area enclosed is not in one plane, if it is like this, half of the area vector will be this way, x axis, half of the area vector will be on the y axis. So it is just simply dot product between two vectors. Now let us take few examples so that we get familiar about how to calculate the magnetic flux. This is represented as phi B. Phi B is integral not closed. It is integral of B dot dA. Now look at dA. There will be many variables. Here it will be equal to magnitude of B into magnitude of dA into cos of angle between B and dA. For right now, this integral has 3 variables B, dA, dA and theta. So will you be able to calculate the integral just like that? Why? Because you can integrate only when there is a single variable. So it becomes extremely difficult to find this integral for a generic case. So it varies case to case very much. And even then, if you are not able to write this integral as a function of one variable, you will not be able to integrate. And it becomes easy for us to integrate this for some few symmetrical cases. Just like in Gauss law, E dot dA integral, we are able to integrate easily for symmetrical cases. Similarly here also, there are few symmetrical cases that will let you calculate this value easily. So let us talk about those cases. Case number one. What do you think the best case will be? Theta is 90. Best case, it becomes 0. Then no matter how B and A are varying, the theta is 90, it is 0. So case number one, theta is 0. Sorry, cos theta is 0 and theta is 90. What do you think case number two will be? Theta is 0 or theta is some constant. That is a 30 degree. Even if it is 30 degree, cos 30, you can take out of integral. So theta should be constant. If theta is constant, this integral becomes what? Now, will you be able to integrate? Can you integrate now? No, still you cannot integrate. So theta is constant and magnitude of B should also be constant. Then you will take B out of integral and this thing will become B into cos theta into integral of dA and integral of dA is what? A. So B into A into cos of theta. When theta will be constant, tell me, if magnetic field direction is fixed, magnetic field direction is fixed, when theta will be constant? Theta is what? And the between area of the loop and magnetic field. The area of the loop will be perpendicular to the loop surface. So when that will happen, when theta will be constant, when area vector is constant, because if area vector also keeps on changing its direction, then theta will be changing and when theta will be constant, when it is a planar surface, it is a surface, it is plane. Then area vector will be, direction of area vector will be constant also. So we will be always on a lookout of case number 1 and case number 2. In fact, since I am calculating this entire flux, this flux I am calculating for the complete loop, I can split this integral into two parts. Magnetic field could be part number 1 B into dA into cos of theta plus integral in part number 2 B into dA into cos of theta and so on. You can split the integral into multiple parts, getting it? Like you can divide the entire loop into multiple parts and you can integrate separately. And if you integrate separately, this integral could be case number 1, this could be case number 2, this could be again case number 1. So like that you can split the integral, entire integral need not be a single case. So what is the cause of the current in a loop? What it is? Change in flux, remember and this is the flux. Take one more thing, write down that flux is defined for the loop. If you do not have a loop, the flux, the meaning of flux is, I mean the flux is meaningless.